Chapter 35, Problem 31A

To connect a pair of resistors so that their equivalent resistance will be less than the resistance of either one, should you connect them in series or in parallel?

To determine

Whether the pair of resistors for less equivalent resistance then each resistance should connect in parallel or series.

Explanation of Solution

Introduction:

In a series circuit, the resistances are simply added to find the equivalent resistance while the inverse of resistances is added to find the equivalent resistance in the parallel circuit.

The inverse of the resistance becomes less than the resistance itself. So, the summation of the resistances in the parallel circuit to find the equivalent resistance also gives the less value of equivalent resistance than the value of each resistance in the parallel circuit.

The resistances are added simply in a series circuit to find equivalent resistance. So, the value of equivalent resistance of the series circuit is always greater than each resistance in the series circuit.

Conclusion:

The pair of resistors should connect in parallel connection to find the less equivalent resistance than each resistance of pair of resistance of the circuit.